Arch Formwork & Centering Calculator
Calculate exact timber rib radii after lagging thickness deductions (R_rib = R_finished − t_lagging), lagging slat quantities, folding strike wedges, and wet masonry dead loads.
Interactive Decentering Wedge Simulator
Adjust the decentering wedge position slider to simulate driving the folding hardwood wedges to smoothly lower the timber frame away from the cured masonry soffit.
Offset-Coordinate "Mark-Out" Table & Interactive Plotter
For large arches where the swing radius exceeds your compass or room length. Simply draw your baseline, measure out horizontal intervals from center (X), and mark vertical height (Y) to plot perfect curves directly on wood or wall.
| Pt # | Dist from Center (X) | Height (Y) | Fraction | Drop |
|---|
Live Plywood Scribing Simulator
🔨 Carpentry Technique: Tap finish brads at coordinate marks. Bend a flexible batten against the pins to scribe a smooth curve.
Formwork Geometry & Lagging Deduction Rules
Subtract the exact thickness of the flexible wood slats to ensure the finished masonry brick course matches the architectural drawing.
Layout the trammel arm pencil at radius R_rib when drawing the cut line on the plywood rib blanks.
Never strike formwork from one side only; symmetrical decentering prevents lateral arch twisting.
Step-by-Step Worked Numeric Example
Suppose you are building timber centering for a brick fireplace opening with a finished span of W = 48.0 inches, finished rise of H = 12.0 inches, and 3/4" (0.75") plywood lagging slats.
Standard Arch Opening Sizes: Quick Reference Table
Pre-calculated dimensions, radius curves, arc lengths, and material recommendations for standard residential and commercial architectural openings.
| Opening Purpose | Span (W) | Rise (H) | Radius (R) | Arc Length (L) | Center Drop | Min Casing Trim | Recommended Substrate |
|---|---|---|---|---|---|---|---|
| Interior Single Door | 30.0" | 6.0" | 21.75" | 33.25" | 15.75" | 3 ft 6 in | 1/4" High-Flex Drywall or Flex Poly |
| Bedroom / Bath Door | 32.0" | 8.0" | 20.00" | 37.10" | 12.00" | 3 ft 10 in | 1/4" High-Flex Drywall / Polyurethane |
| Main Entry / Passage | 36.0" | 9.0" | 22.50" | 41.74" | 13.50" | 4 ft 3 in | 1/4" High-Flex / Kerfed MDF Jamb |
| Hallway / Corridor | 42.0" | 10.5" | 26.25" | 48.70" | 15.75" | 4 ft 10 in | Double 1/4" High-Flex Gypsum |
| Double Doorway / Pass-Through | 48.0" | 12.0" | 30.00" | 55.65" | 18.00" | 5 ft 6 in | Double 1/4" High-Flex or 3/8" Gypsum |
| French Door Opening | 60.0" | 15.0" | 37.50" | 69.56" | 22.50" | 6 ft 8 in | 1/4" Bendable Plywood / Wiggle Board |
| Living Room Cased Archway | 72.0" | 18.0" | 45.00" | 83.47" | 27.00" | 8 ft 0 in | Standard 1/2" Drywall (Wetted) or Plywood |
| Grand Room Divider / Great Hall | 96.0" | 24.0" | 60.00" | 111.30" | 36.00" | 10 ft 6 in | Standard 1/2" Drywall (Dry Bend OK) |
How to Lay Out & Build a Brick Arch: 5-Stage Masonry Guide
Step-by-step master mason guide for constructing rigid timber centering, cutting radial skewbacks, spacing voussoirs, and striking falsework.
Erect & Wedge Timber Centering Formwork
Set the curved timber centering securely between supporting piers. Support centering legs on dual opposing hardwood wedges or sand jacks. Verify the timber crown matches finished springline elevation plus rise minus brick depth.
Layout & Chisel Skewback Abutment Beds
Cut skewbacks directly on supporting piers angled along the true radial sightline toward the curve pivot. Voussoirs must transfer compressive thrust perpendicular to skewback faces, never onto a flat horizontal shelf.
Dry-Fit Voussoirs & Verify Odd Unit Count
Dry-fit all voussoirs along the timber lagging using wood spacer shims. Confirm an ODD total count so a single symmetrical keystone locks the apex. Verify intrados joint width ($t_{int} approx 3/8"$) and extrados taper ($t_{ext} < 1/2"$).
Bed Voussoirs Symmetrically from Springline to Crown
Lay voussoirs in pairs from left and right springlines upward toward the apex. Never lay one side completely first, which distorts centering falsework under uneven thrust. Check every radial joint angle with your pivoted radial story line.
Drive Keystone & Execute Controlled Decentering
Butter both sides of the central keystone with mortar and firmly tap it into the apex gap until flush with adjacent voussoirs. Allow mortar to cure (minimum 48-72 hours). Gently ease opposing falsework wedges symmetrically from center outward to transfer full compressive dead load into abutment piers.
Material Bending Limits & Substrate Specifications
Understand the physical minimum bend radii and structural limitations of gypsum boards, bendable plywood, kerfed jambs, and flexible trim.
1/4" High-Flex Gypsum Board
Specially engineered core with high tensile facing paper. Apply in two laminated 1/4" layers for 1/2" total thickness.
3/8" Standard Drywall
Moderate flexibility. Suitable for wide residential pass-throughs and hallway arches with radius over 5 feet.
1/2" Standard Drywall
Rigid board. Must not be bent dry under 10 ft radius. For wet bending, spray both sides with water and allow to soak for 15 minutes.
1/4" Bendable Plywood (Wiggle Wood)
Multi-ply rotary cut veneer with cross-grain plies omitted. Available in Column Bend (8-ft axis) and Barrel Bend (4-ft axis).
Kerfed 3/4" MDF or Clear Pine
Saw kerfs cut to 5/8" depth (leaving 1/8" face veneer) spaced 1/2" to 3/4" apart. Fill kerfs with PVA glue during mounting for rigidity.
Flexible Polyurethane Moulding
Seamless imitation of wood grain that flexes effortlessly along the intrados. Order based on calculated Arc Length + 10%.
Structural Thrust Dynamics & Lateral Force Engineering
Understand how gravitational loads resolve into outward lateral forces, and how to size king studs, headers, and abutments to prevent framing deflection.
The Fundamental Law of Arch Thrust
The horizontal outward thrust (H_thrust) generated at each springline abutment is inversely proportional to the rise height (H):
Key Rule: Halving the rise height doubles the outward lateral force pushing against your king studs or masonry abutment piers!
General residential partition guidelines. For load-bearing walls, second-story floor loads, or heavy masonry, consult a structural engineer and local building codes (IRC R602).
Semicircular (Roman) Arch
Because the curve meets the springline at a true vertical 90° tangent, the majority of dead load is directed vertically down into the supporting jambs.
Gothic (Pointed) Arch
The pointed apex divides the curve into steeper arcs, reducing horizontal outward vector forces compared to flatter round arches.
Segmental (Shallow) Arch
As the rise decreases relative to the span, the thrust vector angles sharply outward, exerting immense lateral force on the supporting side walls.
Jack (Flat) Lintel Arch
Flat arches rely solely on wedge friction and severe horizontal thrust to hold the voussoirs aloft. Requires massive abutments or structural tie rods.
Common Masonry Voussoir & Centering Mistakes
Prevent apex joint weakness, mortar crushing, and centering collapse during brick arch construction.
Using an Even Number of Voussoirs
Laying an even number of brick wedges in a masonry arch ring, resulting in a weak vertical mortar joint directly at the crown apex.
Always specify an ODD total count of voussoirs so that a solid, symmetrical keystone locks the apex in pure compression.
Using Uniform Thickness Mortar Joints on Curved Rings
Attempting to maintain equal mortar thickness from intrados to extrados without tapering, creating uneven bearing pressure and crushed brick edges.
Calculate wedge taper so intrados joints measure 1/4" to 3/8" while extrados joints widen proportionally based on ring depth, or use gauged wedge-cut bricks.
Improper Skewback Angle on Springline Abutments
Pouring or laying springline skewback skew blocks horizontally rather than perpendicular to the arch radius thrust line, risking horizontal slip.
Cut skewbacks precisely along the radial center line so voussoirs transfer load in 90-degree square compression against the abutment.
Field Master Pro-Tips for Clean Execution
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Frequently Asked Questions
Common carpentry, masonry, and geometric questions regarding arch calculations and construction layout.
Q1 What is arch centering formwork?
Centering (or an arch center) is the temporary timber framework built to support masonry voussoir bricks or stone blocks during construction until the central keystone is driven into place and the mortar cures, making the arch self-supporting.
Q2 How do you calculate the radius of the timber centering rib?
The radius of the timber rib must be deducted by the thickness of the flexible lagging slats attached to its curved top edge. Formula: Rib Radius = Finished Arch Intrados Radius − Lagging Slat Thickness. For a 30.0" finished radius arch with 3/4" (0.75") plywood lagging: Rib Radius = 30.00" − 0.75" = 29.25 inches.
Q3 What are decentering wedges (folding wedges) in arch formwork?
Decentering wedges (or folding wedges) are pairs of opposing hardwood timber wedges placed beneath the temporary vertical support posts. When the mortar cures, the wedges are gently driven inward/outward with a mallet to lower the centering frame smoothly by 1 to 2 inches, transferring compressive loads onto the arch ring without shocking the fresh masonry.
Q4 When is it safe to strike (remove) arch centering formwork?
For standard Portland-lime structural mortar (Type S or M), centering formwork should remain in place for a minimum of 48 to 72 hours in warm weather, and 7 to 14 days for massive stone vault bridges before striking the decentering wedges.